Systems and Methods for Retransmission Return Channel Error Detection

ABSTRACT

A method implemented in a digital subscriber line (DSL) system is described for minimizing a misdetection probability at a far-end coded message receiver during transmission of a coded message. The method comprises jointly determining, at the far-end coded message receiver, a P matrix and a modulation scheme. The method further comprises encoding a message into a coded message with a systematic linear block code, the systematic linear block code having a generator matrix [I P], where I represents a linear block code component identity matrix and P represents the determined P matrix. The method also comprises modulating the encoded message to one or more tones forming a discrete multi-tone (DMT) symbol according to the determined modulation scheme.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of U.S. ProvisionalPatent Application entitled, “Systems and Methods for RetransmissionReturn Channel Error Detection,” having Ser. No. 61/175,351, filed onMay 4, 2009, which is incorporated by reference in its entirety. Thisapplication also claims priority to and the benefit of U.S. ProvisionalPatent Application entitled, “Systems and Methods for RetransmissionReturn Channel Error Detection,” having Ser. No. 61/175,758, filed onMay 5, 2009, which is incorporated by reference in its entirety. Thisapplication also claims priority to and the benefit of U.S. ProvisionalPatent Application entitled, “Systems and Methods for RetransmissionReturn Channel Error Detection,” having Ser. No. 61/178,039, filed onMay 13, 2009, which is incorporated by reference in its entirety. Thisapplication also claims priority to and the benefit of U.S. ProvisionalPatent Application entitled, “Systems and Methods for RetransmissionReturn Channel Error Detection,” having Ser. No. 61/220,970, filed onJun. 26, 2009, which is incorporated by reference in its entirety.

TECHNICAL FIELD

The present disclosure generally relates to digital subscriber line(DSL) systems and specifically, to systems and methods forretransmission return channel error detection.

BACKGROUND

In asymmetric digital subscriber line (ADSL) and very high speed digitalsubscriber line (VDSL) systems, retransmission (ReTx) can be optionallyutilized for ensuring quality of transmission for latency-insensitivedata, such as video. Techniques for performing retransmission areprovided in the G.inp recommendation. The retransmission scheme used inxDSL systems supports both asynchronous transfer mode (ATM) and packettransfer mode (PTM) protocols and has been designed such that elementaryframes that can be retransmitted are formed in the physical layer (PHY).Generally, for ADSL systems, it has been proposed that retransmission beimplemented only in the downstream direction, whereas for VDSL systems,retransmission may either be implemented in strictly the downstreamdirection or in both the downstream and upstream directions.

Generally, a transmitter that supports a retransmission scheme includesa retransmission queue for storing elementary frames in order to haveaccess to previously-sent elementary frames in the event that a requestfor retransmission is received. A request for retransmission iscontained in a retransmission return channel (RRC) message, whichcontains information on which elementary frames have been incorrectlyreceived, and hence need to be retransmitted. RRC messages aretransported over the retransmission return channel. A receiver thatsupports retransmission will typically include a frame error detector, arescheduling queue, and a retransmission request encoder. The frameerror detector detects the correctness of each received frame. Therescheduling queue re-sequences elementary frames in the event thatcorrectly received elementary frames are received out of order due toretransmission. The request encoder converts the decisions of the frameerror detector into a RRC message, which can be understood by thetransmitter side.

For improved robustness during transmission over the retransmissionreturn channel, the request information may be encoded. Encoding, alsoreferred to as coding, involves adding redundancy to the originalmessage. Encoding the RRC message at the receiver side may involve somedecoding capability at the transmitter side in order to be correctlyinterpreted by the system. One technique for encoding the redundancybits of the RRC message has been proposed in the G.inp recommendation.Thus far, the use of a (24,12) extended Golay code and the use of a 12bit cyclic redundancy check (CRC-12) have been proposed to encode the 12bits of the raw RRC message. However, questions remain regarding whichcode performs most effectively for G.inp environments as a number ofperceived shortcomings involving current approaches to utilizing a(24,12) Golay code and a 12-bit cyclic redundancy check (CRC-12) exist.

SUMMARY

One embodiment, among others, is a system that comprises a transmitterfor transmitting a coded message to a far-end coded message receiver.The transmitter comprises an encoder configured to encode a message intoa coded message with a systematic linear block code. The systematiclinear block code has a generator matrix [I P], where I represents alinear block code component identity matrix and P represents a P matrixthat specifies redundancy bits. The transmitter further comprises amodulator configured to modulate the encoded message to one or moretones forming a discrete multi-tone (DMT) symbol, wherein the linearblock code component P matrix and modulation scheme are jointlydetermined to minimize a misdetection probability at the far-end codedmessage receiver.

Another embodiment is a system that comprises a receiver for receiving acoded message from a far-end coded message transmitter. The receivercomprises an error detector configured to determine a level ofcorrectness of the received message encoded with a systematic linearblock code. The systematic linear block code has a generator matrix [IP], where I represents a linear block code component identity matrix andP represents a P matrix that specifies redundancy bits. The receiverfurther comprises a demodulator configured to demodulate the encodedmessage from one or more tones forming a discrete multi-tone (DMT)symbol. The receiver is further configured to transmit modulationinformation associated with the coded message to the far-end messagetransmitter and jointly determines the linear block code component Pmatrix and modulation information to minimize a misdetectionprobability.

Another embodiment is a system for transmitting a 24-bit coded messageto a far-end coded message receiver. The system comprises an encoderconfigured to encode a 12-bit message into a 24-bit coded message with a(24,12) systematic linear block code. The systematic linear block codehas a generator matrix [I P], where I represents a linear block codecomponent identity matrix and P represents a P matrix that specifiesredundancy bits. Furthermore, the linear block code component identitymatrix I is a 12*12 identity matrix, and the component P matrix is

$P = {\begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1\end{bmatrix}.}$

Another embodiment is system for receiving a 24-bit coded message from afar-end coded message transmitter. The system comprises a detectorconfigured to determine a level of correctness of the received 24-bitcoded message, wherein the received 24-bit coded message is encoded witha (24,12) systematic linear block code. The systematic linear block codehas a generator matrix [I P], where I represents a linear block codecomponent identity matrix and P represents a P matrix that specifiesredundancy bits. The linear block code component identity matrix I is a12*12 identity matrix, and the component P matrix is

$P = {\begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1\end{bmatrix}.}$

Another embodiment is a method implemented in a digital subscriber line(DSL) system for minimizing a misdetection probability at a far-endcoded message receiver during transmission of a coded message. Themethod comprises jointly determining, at the far-end coded messagereceiver, a P matrix and a modulation scheme. The method furthercomprises encoding a message into a coded message with a systematiclinear block code, the systematic linear block code having a generatormatrix [I P], where I represents a linear block code component identitymatrix and P represents the determined P matrix. The method alsocomprises modulating the encoded message to one or more tones forming adiscrete multi-tone (DMT) symbol according to the determined modulationscheme.

Other systems, methods, features, and advantages of the presentdisclosure will be or become apparent to one with skill in the art uponexamination of the following drawings and detailed description. It isintended that all such additional systems, methods, features, andadvantages be included within this description, be within the scope ofthe present disclosure, and be protected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the disclosure can be better understood with referenceto the following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the present disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 depicts a functional block diagram of an embodiment for a singlelink retransmission system.

FIG. 2, which illustrates the modulation and demodulation performed inthe physical medium specific (PMD) layer of FIG. 1.

FIG. 3A shows a trellis coded modulation (TCM) encoder.

FIG. 3B illustrates the trellis diagram of the encoding process by a4-state encoder.

FIG. 4 illustrates a flow chart for a TCM encoding procedure for adiscrete multi-tone (DMT) symbol.

FIG. 5A depicts the format of a retransmission return channel (RRC)message and the encoding process.

FIG. 5B depicts the format of a retransmission return channel (RRC)message and the detection process.

FIG. 6 illustrates an embodiment of an apparatus for executing thevarious components shown in FIG. 1.

FIG. 7 depicts a top-level flow diagram for an embodiment of a processfor performing retransmission return channel error detection in thesystem of FIG. 1.

FIG. 8 depicts a flow diagram for an embodiment of a process fordetermining the linear block code P matrix.

FIG. 9 depicts a flow diagram for an embodiment of a process forperforming retransmission return channel error detection in the systemof FIG. 1.

FIG. 10 depicts a flow diagram for another embodiment of a process forperforming retransmission return channel error detection in the systemof FIG. 1.

DETAILED DESCRIPTION

Having summarized various aspects of the present disclosure, referencewill now be made in detail to the description of the disclosure asillustrated in the drawings. While the disclosure will be described inconnection with these drawings, there is no intent to limit it to theembodiment or embodiments disclosed herein. On the contrary, the intentis to cover all alternatives, modifications and equivalents includedwithin the spirit and scope of the disclosure as defined by the appendedclaims.

Various embodiments are described that incorporate a rate ½ systematiclinear block code as an error detection mechanism in the RRC message toaddress performance issues relating to use of the Golay code and CRC-12for error detection in the RRC channel. For some embodiments, thedesired linear block code P matrix is determined by the RRC channelreceiver and communicated to the RRC transmitter during initialization.In other embodiments, the RRC transmitter determines the P matrixfollowing the exchange of information regarding the receiverconfiguration during initialization. Linear block code P matrix valuesare described that are communicated from the RRC receiver to the RRCtransmitter during initialization, or determined prior toinitialization. To avoid transmitting the entire P matrix, a specialmessage identifier is incorporated for some embodiments, where thespecial message identifier is used for selecting pre-stored P matricesfor Golay code, CRC-12 and/or other error correction codes.

Reference is made to FIG. 1, which depicts a functional block diagram ofa single link retransmission system 100 in which embodiments ofretransmission return channel error detection may be implemented. Thesystem 100 comprises a transmitter 102, which comprises a DTU framer 104configured to construct elementary frames, called data transmit units(DTUs) that can be requested for retransmission. Each DTU contains dataprovided by the transport protocol specific transmission convergence(TPS-TC) layer and retransmission (ReTx) specific overhead, which isdescribed in more detail below. The content of each DTU is stored in aretransmission (ReTx) queue 106 prior to being sent to a physical mediumspecific (PMD) layer 109, and then transmitted over the retransmissionforward channel (RFC), which is represented by the solid arrow path inFIG. 1.

The storage of a DTU comprises storing at least the data content of theDTU as well as some or all ReTx specific overhead bytes. The transmitter102 also receives request messages on a retransmission return channel(RRC) represented by the dashed arrow path in FIG. 1. The receivedrequest messages, also called RRC messages, contain information as towhich DTUs have been correctly received and which DTUs need to beretransmitted. For improved robustness during transmission over the RCC,the request information may be coded in a specific format with a requestencoder 114. Note that the request information may need to undergodecoding with a request decoder 108 in order to be correctly interpretedby the system 100.

At the receiver side 110, each DTU is checked for errors after receptionat a DTU error detector 112. Correct DTUs are then passed to a higherlayer. When a DTU is corrupted, a request for retransmission isgenerated by a request encoder 114 and sent on the RRC. When aretransmission is in progress, correctly received DTUs may be storedlocally in a rescheduling queue 116 before being passed to a higherlayer. Such storage ensures a correct ordering of the data passed to thehigher layer. The rescheduling queue 116 then acts as a buffer thatreschedules or re-sequences DTUs received out-of-sequence. At thetransmitter side 102, the PMD layer 109 modulates data sent over the RFCand demodulates data received from the RRC. At the receiver side 110,the PMD layer 111 demodulates data received from the RFC and modulatesdata sent over the RRC.

Reference is now made to FIG. 2, which illustrates the modulation anddemodulation performed in the PMD layer 109, 111, commonly referred toas discrete multi-tone (DMT) modulation and demodulation. In DMTmodulation, the input bits of the PMD layer 109, 111 are encoded by aninner coded modulation scheme into amplitude and phase informationsignals x_(k)(q) (i.e., complex numbers taken from a finite size2-dimensional constellation) alternately carried over the subcarrierfrequency band, also referred to as the tone, specified by the index qin the integer set {1,2, . . . , Q}. The number Nq of bits mapped tox_(k)(q)x_(k)(q) depends on the transmission quality relative to thetone q, and is dictated by a bit-loading algorithm. For improvedperformance, the inner coded modulation output bits are not necessarilymapped to tones with contiguous indices q. The tone indices may beinterleaved with a pattern dictated by the tone interleaving algorithm.The “modulation information” formed by the combination of the bitloading and tone interleaving information, which may comprise“bit-to-tone” loading information, is exchanged between the DSLtransceivers at initialization. At the coded modulation scheme output,each block of Q contiguous complex signals x_(k)(1), . . . , x_(k)(Q)forms a frequency-domain DMT symbol of index k, which is transformed viaan IFFT (inverse fast Fourier transform) block 204 into a discrete timesequence. A cyclic prefix adder 206 then adds a cyclic prefix, alsoreferred to as guard interval, to the output of the IFFT block 204 toimprove robustness to inter symbol interference. Finally, a front-enddevice 216 transforms the discrete time sequence into a continuous timesignal sent to the channel. The processing done in the front-end device216 typically combines both digital and analog domain processing.

In DMT demodulation, the front-end device 216 receives time domainsamples from the channel. After cyclic prefix removal at the cyclicprefix remover 214, the signal is forwarded to a FFT (fast Fouriertransform) block 212. For each received DMT symbol of index k, the FFTblock 212 outputs a complex information y_(k)(q) per tone q for all q inthe integer set {1,2, . . . , Q}. The information y_(k)(q) is thenequalized by the frequency domain equalizer (FEQ) block 210, whichtypically processes independently each tone using a one-tap complexequalizer, and then feeds the signal to a coded modulation decoder 208for the inner coded modulation scheme. The decoder 208 output contains adecision on the bits that constitute the PMD 109, 111 output. The codedmodulation scheme typically used in xDSL systems is a four-dimensional(4D) 16-state Wei trellis coded modulation (TCM) scheme. The TCM encoder300 is depicted in FIG. 3A, and for some embodiments, comprises a rate(Nq+Nq′−1)/(Nq+Nq′) 16-state systematic convolutional encoder device 302and an Nq*Nq′ 4D quadrature amplitude modulation (QAM) constellationmapper device 304. The 4D QAM mapper 304 generates a 4D signal formed bytwo 2D QAM signals x_(k)(q) and x_(k)(q′) that are mapped to a pair oftones {q,q′}. Note that the tones q and q′ are not necessarilycontiguous, as the mapping of 2D QAM signals to tones may be interleavedfor improved performance. The signals x_(k)(q) and x_(k)(q′) containrespectively Nq and Nq′ bits, i.e., are taken from a 2D QAMconstellation with 2^(Nq) and 2^(Nq′) possible points, respectively. Thevalues of Nq and Nq′ depend on the output of the bit-loading algorithm,may take any integer value from 1 to 15, and may change from one 4Dsignal to another.

The encoding process is generally represented by a trellis diagram, asseen in FIG. 3B for a 4-state encoder, in which each trellis sectionrepresents the transition from one state to another, the transitionbeing decided by the particular combination of the Nq+Nq′−1 input bits.Each new set of Nq+Nq′−1 input bits leads to a transition to the nextsection in the trellis diagram. A TCM encoding process 400 for a DMTsymbol is shown in FIG. 4 and involves the following. Beginning withblock 410, the convolutional encoder state is initialized to an all-zerostate. The first set {q,q′,Nq,Nq′} is then derived from the bit-loadingalgorithm and Nq+Nq′−1 bits are fetched from the encoder input andencoded. In block 420, the next set {q,q′,Nq,Nq′} is derived from thebit-loading algorithm and Nq+Nq′−1 new bits are fetched from the encoderinput and encoded (block 430). The process is continued until all thetones of a DMT symbol (i.e., until all values between 1 and Q have beentaken either by q or q′) are mapped (decision block 440). Note that thelast bits of the encoder input can be set to a value that forces theencoder state to reach an all-zero state, thereby improving the TCMdecoding performance and automatically reinitializes the state for thenext DMT symbol.

For some embodiment, the decoding algorithm for the TCM code can bebased on the Viterbi algorithm, The Viterbi algorithm searches thetrellis diagram for the most likely path to have been generated by theinput sequence. Note that when the encoder is initialized to a knownstate (say all-zero state), the number of possible transitions to in thefirst sections of the trellis diagram is reduced (as shown on theleft-end side of FIG. 3B). Therefore, knowing the starting state reducesthe number of possible trellis branches to search with the Viterbialgorithm, thereby reducing the probability of decision error for thebits mapped to the associate sections.

FIG. 5A depicts the format of a retransmission return channel (RRC)message and the encoding process. An n-bit RRC message or coded messageis formed by k information bits 502 (which contain actual informationrelative to which DTU has been correctly or incorrectly received) andr=n−k redundancy bits that contain no new information and that are alinear combination of the information bits. The code used to generatethe message is characterized as being “systematic,” since the codedmessage 508 contains the original (unmodified) k information bits 502.The original information 502 can be recovered from the coded message 508by simply truncating the first k bits of the coded message. The requesttransmitter located in the receiver block 110 may encode a n-bit RRCmessage by performing a matrix multiplication 504 between the uncodedk-bit message and a k*n generator matrix G=[I_(k) P], where I_(k) is thek*k identity matrix and P is the k*r matrix that determines theredundancy bits. In the current xDSL standard, a RRC message is sent ineach DMT symbol, where the n-bits forming the message are the first bitsto be sent to the TCM encoder.

FIG. 5B depicts the format of a retransmission return channel (RRC)message and the detection process. The RRC receiver 110 may detectcorrupted RRC messages by checking for a non-zero syndrome, where thesyndrome may be computed by matrix multiplication of received messagewith the n*r parity check matrix H=[P^(T) I_(r)]^(T), where the notation^(T) denotes the transpose operator. The values of n and k proposed sofar for current standard xDSL (ADSL and VDSL) systems are k=12 and n=24.But the following concepts can be extended to any values of n and k, forn>k. So far, a proposed method for performing xDSL encoding on the RRCmessage is directed to using (n=24, k=12) extended Golay code or a(n=24, k=12) systematic code whose redundancy part can be generated witha 12-bit cyclic redundancy check code (CRC-12) applied to theinformation bits. For example, the P matrix for a CRC-12 with generatorpolynomials x¹²+x¹¹+x³+x²+x+1 is given by the following:

$\begin{matrix}{P = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 \\1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\1 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1\end{bmatrix}} & (1)\end{matrix}$

For example, a (24,12) extended Golay code may be implemented with thefollowing matrix:

$\begin{matrix}{P = \begin{bmatrix}1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 \\1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 \\0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 \\0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 \\1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0\end{bmatrix}} & (2)\end{matrix}$

One approach comprises a theoretical comparison of the detectionperformance of cyclic redundancy check (CRC) versus that of block codes.Binary (n,k) block codes are roughly equivalent to a CRC-(n−k) whenexamined from the standpoint of trade-off between bandwidth efficiencyand detection performance.

More practical results on the detection performance of a CRC-12 and the(24,12) extended Golay code are now described. Specifically, detectionperformance results obtained via Monte-Carlo simulation are discussedalong with results obtained with a retransmission scheme emulated inMatlab/C. A study of the misdetection probability of an r-bit CRC (alsoreferred as CRC-r) and an (n, k) binary block code was performed, andthe study assumed uniformly distributed (i.e., each of the possible2^(n) combinations of n-bit noise pattern has a probability 2^(−n))error pattern and concluded that both CRC and block code have amisdetection probability:

P _(mis)˜2^(−r)(=2.44e−4 for r=12 bits)   (3)

In practice, however, the error patterns experienced by the RRC aregenerally not uniformly distributed. These error patterns depend mainlyon the noise on the line (impulse power relative to stationary noise),the inner code (whether TCM is used or not) and the constellationmapping. Monte-Carlo simulation results obtained with a system emulatedin Matlab/C are described. With the Monte-Carlo simulations, themisdetection probabilities of CRC with generator polynomialx¹²+x¹¹+x³+x²+x+1 and extended (24,12) Golay cod were calculated in thedifferent simulation setups.

The simulation setup comprised a DMT symbol formed by 24 tones loadedwith the same constellation. DMT symbols were either loaded with allQPSKs (small size constellations), all 7-bit QAMs (medium sizeconstellations), or all 12-bit QAM (large size constellations). Standard16-state Wei TCM enabled was used. Finally, impulse noise was emulatedby applying a background AWGN of power equal to the loading SNR for 10⁻⁷BER (including TCM coding gain) increased by an ImpulseNoisePowervarying from 4 to 24 dB by step of 10 dB.

The results are shown below where Tables 1 and 2 provide the number

Y of corrupted RRCs received and the number X of misdetections, as wellas the misdetection rate Z=X/Y. In the tables below, the followingnotation is used: ‘X in Y→Z’. This represents X misdetections thatoccurred in Y corrupted received RRC messages that led to a misdetectionrate Z.

TABLE 1 Simulated misdetection probability for CRC-12 ImpulseNoisePower4 dB 14 dB 24 dB QPSK 100 in 2.1 · 10⁵ 252 in 8.2 · 10⁵ 178 in 7.3 · 10⁵→ 4.7 · 10⁻⁴ → 3.1 · 10⁻⁴ → 2.4 · 10⁻⁴  7-bit QAM 6 in 2 · 10⁵ → 110 in3.5 · 10⁵ 62 in 2.7 · 10⁵ 3 · 10⁻⁵ → 3.1 · 10⁻⁴ → 2.3 · 10⁻⁴ 12-bit QAM0 in 8 · 10⁶ → 0 43 in 8 · 10⁶ → 29 in 3 · 10⁵ → 5.4 · 10⁻⁶ 9.7 · 10⁻⁵

TABLE 2 Simulated misdetection probability for (24, 12) Golay codeImpulseNoisePower 4 dB 14 dB 24 dB QPSK 7 in 2.1 · 10⁵ → 175 in 8.2 ·10⁵ 185 in 7.3 · 10⁵ 3.3 · 10⁻⁵ → 2.1 · 10⁻⁴ → 2.5 · 10⁻⁴  7-bit QAM 2in 2 · 10⁵ → 55 in 3.5 · 10⁵ 61 in 2.7 · 10⁵ 1 · 10⁻⁵ → 1.6 · 10⁻⁴ → 2.3· 10⁻⁴ 12-bit QAM 8 in 8 · 10⁶ → 211 in 8 · 10⁶ 42 in 3 · 10⁵ → 1 · 10⁻⁶→ 2.6 · 10⁻⁵ 1.4 · 10⁻⁴

As shown in the simulation results above, the performance associatedwith using the Golay code and CRC-12 varies. In general, the Golay codeperforms better when the RRC is mapped on small or medium-sizedconstellations. This is not unexpected because due to its Hamming weightdistribution and particularly, the increased minimum Hamming distance,the Golay code is expected to perform better in the presence ofrandom-like errors. In general, the CRC performs better when the RRC ismapped on large constellations. For large constellations, errors aremore likely to be grouped into bursts, and hence are more likely to bedetected with the CRC. Additionally, both techniques exhibit similarperformance. Both techniques converge toward the theoretical performancein Equation (3) when the noise power increases, and hence become moresimilar in high-power impulse noise environments. Also, both techniquesexperience a decrease in the misdetection probability when the impulsenoise power decreases.

The reason the CRC-12 (x¹²+x¹¹+x³+x²⁺x⁺1) exhibits better performance asthe constellation size increases is that the error patterns seen by theRRC message are less random (i.e., are more bursty) due to pathselection in the inner code (TCM) trellis combined with the QAMconstellation mapping. Therefore, in this situation, use of the CRC-12is more appropriate. In this regard, the Golay code and CRC-12 exhibitdifferent performance, depending on the noise power and the bit-loading.Furthermore, the lowest misdetection probability rates were obtainedwith a CRC-12 by loading the RRC message on large constellations(typically 12-bits or larger size). Therefore, the misdetectionprobability of the Golay code can be matched or even improved by using aCRC-12 and ensuring that the RRC message is loaded on a pair of tonescomprising 12 or more bits.

In view of the foregoing, various embodiments are directed to a RRCreceiver 110 configured to select the redundancy technique (i.e., a Pmatrix) that more effectively reduces the misdetection probabilityaccording to the system setup, which mainly comprises the bit-loadingassociated with the modulated RRC message, and the noise environment interms of the expected impulse noise power. In other embodiments, theselection of the redundancy technique can be done by the RRC transmitter102 following prior information exchange of the configuration of thereceiver—in particular, after exchange of the bit-loading information onwhich the RRC will be mapped/demapped.

Note that for some system configurations (bit-loading, impulse noisepower, inner coding, etc.), neither the previously defined Golay norCRC-12 as previously defined appears to be the optimum coding techniqueto minimize the misdetection probability. Various embodiments areproposed that incorporate a different P matrix that minimizes themisdetection probability. In order to extend the number of possiblecodes for the RRC message error detection mechanism to codes other thanthe two codes described above (i.e., Golay code or CRC-12), an expansionof the possible choice of systematic linear block codes where thegenerator matrix can be expressed in the form G=[I_(k) P] is nowdescribed.

Various embodiments are described that utilize rate ½ (i.e., r=k)(24,12) codes. Specifically, various embodiments are directed toutilizing a linear block code P matrix determined by a RRC channelreceiver 102 and communicated to the RRC transmitter 110 during aninitialization phase. In other embodiments, a RRC transmitter 110determines the P matrix based on information relating to the receiverconfiguration exchanged during an initialization phase. One perceivedshortcoming with the approaches described earlier is that the previouslydetermined P matrices do not systematically minimize the misdetectionprobability. To this end, various embodiments are directed toincorporating alternative P matrices obtained by permuting columns ofthe P matrix (2) described earlier.

Generally, the misdetection performance of a code depends on itsEuclidean distance spectrum, that is, the distribution of themisdetection points in the Euclidean space. A misdetection point is amulti-dimensional QAM signal that is different than the transmitted oneand that will lead to the all-zero syndrome when decoded at the receiverside. In this case, the all-zero syndrome leads to a misdetection. Basedon the Euclidean distance spectrum, the misdetection probability can beupper-bounded by the union bound as is expressed as follows:

P _(mis)<=Σ_(δ) A _(δ) *Q(sqrt(δ/σ² /E _(av)))   (4)

where δ represents the squared Euclidean distance between signals in theodd integer lattice (square lattice with points only at oddcoordinates), A_(δ) is the number of couples {transmitted signal,misdetection signals} that are distant by the square distance δ, E_(av)is the average energy of the constellation mapping the codeword, and σ²is the noise variance. The Q function ties the Euclidean distance andthe actual misdetection probability.

The table below shows the smallest multiplicities of the Euclideandistance spectrum of the code described above mapped to the standard12*13 bits TCM coded 4D QAM.

TABLE 3 Euclidean distance spectrum of the Golay code with P matrix (2)δ 16 24 32 40 48 56 64 72 80 88 96 104 A_(δ) 0 48 0 0 26 98 256 56 60436 0 52The codeword is mapped on this constellation because the 12*13 bits4D-QAM is the smallest constellation size formed by the smallestcomponent 2D-QAM constellations that allows mapping of the 24-bit RRCmessage on the smallest number of tones (i.e., 2). Note that the benefitis twofold. First, smaller constellations are less sensitive to noise.Second, mapping to a smaller number of tones, and especially only 2tones, reduces the TCM decoder output error probability because the RRCis mapped to the first section of the TCM code trellis. The firstsection of the TCM code trellis is less likely to generate errorsbecause the starting TCM trellis state is known (i.e., equals zero).Information regarding the starting state aids in the decision process bythe TOM decoder (based on the Viterbi algorithm) by reducing the numberof possible trellis branches to search.

Mapping the full RRC message to the first section of the inner codetrellis eliminates some possible error patterns that corrupt the RRCmessage, thereby reducing the RRC message error probability. Reducingthe RRC error probability reduces the chances of misdetection, therebyimproving the overall detection performance. Robustness to errors canalso be improved by modulating the RRC message to tones with asignal-to-noise ratio (SNR) higher than a minimum necessary SNR requiredto guarantee the targeted error rate of the RRC message. In DSL, theminimum necessary SNR must guarantee a target Bit Error Rate of 10E-7 Byfixing the constellation as proposed above, the resulting reduced spaceof error patterns may in turn lead to the derivation of specificoptimized P matrices minimizing the misdetection probability.

A Golay code with an alternative P matrix provides better performance ina low noise power scenario. The Q function referred in Equation (4) is arapidly decreasing function. As a consequence, the misdetectionprobability depends more on the smallest distances δ and associatemultiplicities A_(δ). With a high signal-to-noise ratio (i.e., a lownoise power), the misdetection probability mostly depends on the minimumsquared Euclidean distance δ_(min)between misdetection points and itsassociate multiplicity A_(δmin). Therefore, various embodiments aredirected to maximizing the minimum Euclidean distance as a criterion foroptimizing a code for low noise power scenarios.

With a minimum squared Euclidean distance δ_(min)=24, note that theGolay code with the P matrix (2) described earlier does not provideoptimum performance. For example, the Golay code with the P matrix

$\begin{matrix}{P = \begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 \\1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 \\1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 1 \\1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 \\0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 \\1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 \\0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 \\1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1\end{bmatrix}} & (5)\end{matrix}$

leads to a minimum squared Euclidean distance δ_(min)=40 (cf. Euclideandistance spectrum in Table 2).

TABLE 4 Euclidean distance spectrum of the Golay code with P matrix (5)δ 16 24 32 40 48 56 64 72 80 88 96 104 A_(δ) 0 0 0 10 0 280 264 20 6 4240 116

With medium-range SNRs or medium noise levels, the misdetectionprobability depends not only on the minimum squared Euclidean distanceδ_(min) and its associate multiplicity A_(δmin), but also on the nextdistances as well as the number of multiplicities associated with smalldistances. For this range of SNRs, various embodiments incorporate acode having a reduced total number of multiplicities associated withsmall distances than just a large minimum distance. For example, theGolay code with the P matrix below

$\begin{matrix}{P = \begin{bmatrix}0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 \\0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 \\1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 \\1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 1 \\1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 1 & 1 \\0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 \\1 & 0 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 \\0 & 1 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1\end{bmatrix}} & (6)\end{matrix}$

outperforms the code with the P matrix (5) in the range of medium SNRs.As seen in Table 5, for P matrix (6), there is only 208 misdetectionpoints located at a squared Euclidean distance smaller than 104, ascompared to 1120 points for the matrix (5).

TABLE 5 Euclidean distance spectrum of the Golay code with P matrix (6)δ 16 24 32 40 48 56 64 72 80 88 96 104 A_(δ) 4 0 0 0 2 0 0 22 104 46 426

For high power noise, it can be assumed that all misdetection points areequiprobable, thereby leading to uniformly distributed error patterns.Each of the possible 2^(n) combinations of n-bit noise pattern has aprobability 2^(−n). This leads to the misdetection probability

P _(min)˜2⁻¹²=2.44e−4   (7)

To illustrate the concepts described above, Monte-Carlo simulationresults are now discussed. The misdetection probabilities of the Golaycode with various P matrices were calculated by Monte-Carlo simulationin the different simulation setups. In one setup, the 24-bit message(becoming 25 bits after TCM encoding) was mapped to 12*13 bits 4D-QAMconstellations. DMT symbols are formed by 24 tones loaded with the same12*13 bits 4D-QAM constellations. Standard 16-state Wei TCM is used.Impulse noise was emulated by applying a background AWGN of power equalto the loading SNR for 10⁻⁷ BER (including TCM coding gain) increased byan ImpulseNoisePower varying from 4 to 24 dB by step of 10 dB.

Table 6 provides the number Y of corrupted codewords received and thenumber X of misdetections, as well as the misdetection rate Z=X/Y. Inthe tables, the notation ‘X in Y→Z’ represents X misdetections thatoccurred in Y corrupted received RRC messages leading to a misdetectionrate Z.

TABLE 6 Simulated misdetection probability for Golay code with various Pmatrices ImpulseNoisePower 4 dB 14 dB 24 dB P matrix (2) 8 in 8 · 10⁶ →211 in 8 · 10⁶ 42 in 3 · 10⁵ → 1 · 10⁻⁶ → 2.6 · 10⁻⁵ 1.4 · 10⁻⁴

It should be emphasized that while the P matrix given in Equation (2) isoptimal in terms of Hamming distance properties, it is not optimal interms of Euclidean distance properties. The Euclidean distanceproperties of the Golay code with the generator matrix G based on the Pmatrix given in equation (2) can be altered by permuting the redundancybits obtained by multiplication of message and the matrix G. Thisoperation does not change the code Hamming distance properties. Anequivalent result can be obtained by permuting the columns of the GolayP matrix. Experimentally, the minimum squared Euclidean distance δ_(min)can be calculated for all 12! permutations of the columns of the Golaymatrix given in equation (2). The maximum δ_(min) was found by applyingthe permutation operation (12 4 7 2 1 11 10 6 3 8 9 5) to the columns ofthe Golay matrix. The resultant Golay matrix is given by equation (8).

$\begin{matrix}{P = \begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1\end{bmatrix}} & (8)\end{matrix}$

The P matrix (8) in the equation above yields the same Hamming distanceproperty than the Golay matrix shown in Equation (2), but yieldsimproved Euclidean distance properties. The optimized P matrix yields aminimum squared Euclidean distance δ_(min)=112. By comparison, the Golaymatrix of equation (2) so far yields a minimum Euclidean distance ofδ_(min)=24, where minimum squared Euclidean distance computation assumes12*13 bits 4D-QAM constellations and 1 TCM redundancy bit per 4D QAMsignal.

FIG. 6 illustrates an embodiment of an apparatus for executing thevarious components shown in FIG. 1. Generally speaking, the variousembodiments for performing retransmission return channel error detectionmay be implemented in any one of a number of computing devices.Irrespective of its specific arrangement, the retransmission system 100in FIG. 1 may comprise memory 612, a processor 602, and mass storage626, wherein each of these devices are connected across a data bus 610.

The processor 602 may include any custom made or commercially availableprocessor, a central processing unit (CPU) or an auxiliary processoramong several processors associated with the retransmission system 100,a semiconductor based microprocessor (in the form of a microchip), oneor more application specific integrated circuits (ASICs), a plurality ofsuitably configured digital logic gates, and other well known electricalconfigurations comprising discrete elements both individually and invarious combinations to coordinate the overall operation of thecomputing system.

The memory 612 can include any one or a combination of volatile memoryelements (e.g., random-access memory (RAM, such as DRAM, and SRAM,etc.)) and nonvolatile memory elements (e.g., ROM, hard drive, CDROM,etc.). The memory 612 typically comprises a native operating system 614,one or more native applications, emulation systems, or emulatedapplications for any of a variety of operating systems and/or emulatedhardware platforms, emulated operating systems, etc. For example, theapplications may include application specific software 616 stored on acomputer readable medium and executed by the processor 602 and mayinclude any of the components described with respect to FIGS. 1 and 2.One of ordinary skill in the art will appreciate that the memory 612can, and typically will, comprise other components which have beenomitted for purposes of brevity. It should be noted, however, that thevarious components in FIGS. 1 and 2 may also be embodied as hardware.

Where any of the components described above comprises software or code,these components are embodied in a computer-readable medium for use byor in connection with an instruction execution system such as, forexample, a processor in a computer system or other system. In thecontext of the present disclosure, a computer-readable medium refers toany tangible medium that can contain, store, or maintain the software orcode for use by or in connection with an instruction execution system.For example, a computer-readable medium may store one or more programsfor execution by the processing device 602 described above.

More specific examples of the computer-readable medium may include aportable computer diskette, a random access memory (RAM), a read-onlymemory (ROM), an erasable programmable read-only memory (EPROM, EEPROM,or Flash memory), and a portable compact disc read-only memory (CDROM).As shown in FIG. 6, the retransmission system 100 may further comprisemass storage 626. For some embodiments, the mass storage 626 may includea database 628 for storing and managing data, such as bit-loadingtables.

FIG. 7 depicts a top-level flow diagram 700 for an embodiment of aprocess for performing retransmission return channel error detection inthe system of FIG. 1. For this embodiment, a method is implemented in adigital subscriber line (DSL) system for performing error detection in aretransmission return channel (RRC) message. The method comprisesdetermining a linear block code P matrix at a RRC receiver (block 710),transmitting an identifier corresponding to the linear block code Pmatrix to a RRC transmitter (720), and selecting, at the RRCtransmitter, the determined P matrix according to the identifier (block730). For some embodiments, the identifier may contain differentinformation, including but not limited to the row and column entries ofthe P matrix, the permutation pattern according to a reference P matrixknown a priori by the RRC receiver and an index to be used to select theP matrix among a pre-stored table of P matrices.

FIG. 8 depicts a flow diagram 800 for an embodiment of a process fordetermining the linear block code P matrix. The process begins with theinput of the RRC message codeword length n and information length k, andthe dimension N of the inner TCM (block 805) and is performed in twophases. The first phase comprises selecting a mapping strategy forminimizing the RRC message error probability. The mapping strategy isdirected to mapping the RRC message to the first trellis section of theTCM, which involves selecting an N-dimensional QAM constellation thatcan map n+1 bits (block 810).

The second phase comprises minimizing the misdetection probability ofcorrupted RRC messages. This second phase comprises first finding a Pmatrix yielding a code that is optimal in the Hamming space, i.e., witha maximized minimum Hamming distance (block 820). Then, for eachpossible permutation of the P matrix (block 830), compute the firstelements of the Euclidean distance spectrum for a k-bit informationmessage first encoded with the block code based on the permuted Pmatrix, then TCM coded and mapped to the selected N-dimensional QAMconstellation (block 840). The process outputs the permuted P matrixbest fitting a selection criterion.

The selection criterion (decision block 850, block 860) in FIG. 8involves selecting the permutation leading to the largest minimumEuclidean distance. This criterion is best suited for an environmentwith a high impulse noise to signal power ratio. The criterion maychange for environments with medium and low impulse noise to signalpower ratio. Another criterion better suited for an environment with amedium range of impulse noise to signal power ratio involves selectingthe permutation leading to the smallest total number of multiplicitiesassociated with small distances in the Euclidean distance spectrum. Thesteps described above, beginning with block 830, are repeated until all(n−k)! (factorial) column permutations are processed (decision block870). The parameter Pbest is then output (block 875).

FIG. 9 depicts a flow diagram 900 for an embodiment of a process forperforming retransmission return channel error detection in the systemof FIG. 1. For this embodiment, a method is implemented in a digitalsubscriber line (DSL) system for performing error detection in aretransmission return channel (RRC) message. The method comprisesdetermining a bit loading at a RRC receiver such that the n+1 bitscontaining the TCM coded RRC message are mapped to the first trellissection of the TCM trellis diagram (block 910), transmitting the bitloading indication to a RRC transmitter (920), and selecting, at the RRCtransmitter, the bit loading for the tones carrying the RRC messageaccording to the indication received from the RRC receiver (block 930).

FIG. 10 depicts a flow diagram 1000 for another embodiment of a processfor performing retransmission return channel error detection in thesystem of FIG. 1. In accordance with some embodiments, a process isimplemented in a digital subscriber line (DSL) system for minimizing amisdetection probability at a far-end coded message receiver duringtransmission of a coded message. Beginning with block 1010, the methodcomprises jointly determining, at the far-end coded message receiver, aP matrix and a modulation scheme. The method further comprises encodinga message into a coded message with a systematic linear block code, thesystematic linear block code having a generator matrix [I P], where Irepresents a linear block code component identity matrix and Prepresents the determined P matrix (block 1020). The method alsocomprises modulating the encoded message to one or more tones forming adiscrete multi-tone (DMT) symbol according to the determined modulationscheme (block 1030).

It should be emphasized that the above-described embodiments are merelyexamples of possible implementations. Many variations and modificationsmay be made to the above-described embodiments without departing fromthe principles of the present disclosure. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and protected by the following claims.

1. A system comprising: a transmitter for transmitting a coded messageto a far-end coded message receiver, the transmitter comprising: anencoder configured to encode a message into a coded message with asystematic linear block code, the systematic linear block code having agenerator matrix [I P], where I represents a linear block code componentidentity matrix and P represents a P matrix that specifies redundancybits; and a modulator configured to modulate the encoded message to oneor more tones forming a discrete multi-tone (DMT) symbol, wherein thelinear block code component P matrix and modulation scheme are jointlydetermined to minimize a misdetection probability at the far-end codedmessage receiver.
 2. The system of claim 1, wherein the transmitter isconfigured to minimize the misdetection probability by selecting themodulation scheme to minimize the message error probability and thenselecting the component P matrix that maximizes both Hamming andEuclidean minimum distances on the coded message.
 3. The system of claim1, wherein the transmitter is configured to minimize the misdetectionprobability by selecting a modulation scheme to minimize the messageerror probability.
 4. The system of claim 3, wherein the message errorprobability is minimized by modulating the coded message to tones with asignal-to-noise ratio (SNR) higher than the minimum required SNR.
 5. Thesystem of claim 1, wherein upon selecting a modulation scheme, thetransmitter then selects the component P matrix that maximizes a Hammingminimum distance and minimizes multiplicities associated with smallestEuclidean distances of a Euclidean distance spectrum computed for thecoded message.
 6. The system of claim 1, wherein the linear block codecomponent P matrix is communicated by the far-end coded messagereceiver.
 7. The system of claim 1, wherein configuration of themodulator is specified by the far-end message receiver.
 8. The system ofclaim 1, wherein the joint determination of the linear block codecomponent P matrix and modulation scheme is performed according to anoise environment.
 9. The system of claim 7, wherein the configurationof the modulator comprises bit-to-tone loading information.
 10. Thesystem of claim 1, wherein the modulator operates based on a trelliscoded modulation (TCM) scheme, wherein the message error probability isminimized by modulating the coded message including the TCM redundancyto a first trellis section of a TCM trellis diagram.
 11. A systemcomprising: a receiver for receiving a coded message from a far-endcoded message transmitter, the receiver comprising: an error detectorconfigured to determine a level of correctness of the received messageencoded with a systematic linear block code, the systematic linear blockcode having a generator matrix [I P], where I represents a linear blockcode component identity matrix and P represents a P matrix thatspecifies redundancy bits; and a demodulator configured to demodulatethe encoded message from one or more tones forming a discrete multi-tone(DMT) symbol; and wherein the receiver is further configured to transmitmodulation information associated with the coded message to the far-endmessage transmitter, and wherein the receiver jointly determines thelinear block code component P matrix and modulation information tominimize a misdetection probability.
 12. The system of claim 11, whereinthe linear block code component P matrix is communicated to the far-endcoded message transmitter.
 13. The system of claim 11, wherein thedemodulator comprises a trellis coded modulation (TCM) scheme decoder.14. The system of claim 13, wherein the receiver minimizes the messageerror probability by transmitting to the far-end transmitter, modulationinformation to modulate the coded message including the TCM redundancyto a first trellis section of a TCM trellis diagram.
 15. The system ofclaim 11, wherein the receiver minimizes the message error probabilityby transmitting to the far-end transmitter, modulation information tomodulate the coded message to tones with a signal-to-noise ratio (SNR)higher than the minimum required SNR.
 16. The system of claim 11,wherein the receiver minimizes the misdetection probability by selectinga modulation scheme that minimizes the message error probability. 17.The system of claim 16, wherein upon selecting a modulation scheme, thereceiver then selects the component P matrix that maximizes both Hammingand Euclidean minimum distances computed for the coded message.
 18. Thesystem of claim 16, wherein upon selecting a modulation scheme, thereceiver then selects the component P matrix that maximizes the Hammingminimum distance and minimizes multiplicities associated with smallestEuclidean distances of a Euclidean distance spectrum computed for thecoded message.
 19. A system for transmitting a 24-bit coded message to afar-end coded message receiver, comprising: an encoder configured toencode a 12-bit message into a 24-bit coded message with a (24,12)systematic linear block code, the systematic linear block code having agenerator matrix [I P], where I represents a linear block code componentidentity matrix and P represents a P matrix that specifies redundancybits, wherein the linear block code component identity matrix I is a12*12 identity matrix, and wherein the component P matrix is:$P = {\begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1\end{bmatrix}.}$
 20. A system for receiving a 24-bit coded message froma far-end coded message transmitter, comprising: a detector configuredto determine a level of correctness of the received 24-bit codedmessage, wherein the received 24-bit coded message is encoded with a(24,12) systematic linear block code, the systematic linear block codehaving a generator matrix [I P], where I represents a linear block codecomponent identity matrix and P represents a P matrix that specifiesredundancy bits, wherein the linear block code component identity matrixI is a 12*12 identity matrix, and wherein the component P matrix is:$P = {\begin{bmatrix}1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 \\1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \\1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\0 & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 \\1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1\end{bmatrix}.}$
 21. A method implemented in a digital subscriber line(DSL) system for minimizing a misdetection probability at a far-endcoded message receiver during transmission of a coded message,comprising: jointly determining, at the far-end coded message receiver,a P matrix and a modulation scheme; encoding a message into a codedmessage with a systematic linear block code, the systematic linear blockcode having a generator matrix [I P], where I represents a linear blockcode component identity matrix and P represents the determined P matrix;and modulating the encoded message to one or more tones forming adiscrete multi-tone (DMT) symbol according to the determined modulationscheme.
 22. The method of claim 21, wherein jointly determining a Pmatrix and a modulation scheme comprises: selecting a modulation schemethat minimizes the misdetection probability; and upon selecting themodulation scheme, selecting the P matrix that maximizes both Hammingand Euclidean minimum distances, wherein the minimum Euclidean distanceis computed for the coded message.